Below are listed rank-two temperaments supported by the 22edo patent val, below the indicated cutoff in TE badness.

5-limit temperaments with badness below 0.1

Listed is the wedgie and the TE complexity for six temperaments with badness less than 0.1.

Rank	Wedgie	Name	Complexity	Commas
1	<<3 5 1]]	Porcupine	1.663	250/243
2	<<2 -4 -11]]	Srutal	2.121	2048/2025
3	<<5 1 -10]]	Magic	2.417	3125/3072
4	<<7 -3 -21]]	Orson	4.232	2109375/2097152
5	<<9 -7 -32]]	Escapade	6.243	4294967296/4271484375
6	<<16 -10 -53]]	Kwazy	10.454	9010162353515625/9007199254740992

7-limit temperaments with badness below 0.06

Listed is the wedgie and the TE complexity for 14 temperaments with badness less than 0.06.

Rank	Wedgie	Name	Complexity	Commas
1	<<2 -4 -4 -11 -12 2]]	Pajara	1.953	50/49 64/63
2	<<6 10 10 2 -1 -5]]	Hedgehog	2.784	50/49 245/243
3	<<3 5 -6 1 -18 -28]]	Porcupine	2.819	64/63 250/243
4	<<1 9 -2 12 -6 -30]]	Superpyth	2.874	64/63 245/243
5	<<8 6 6 -9 -13 -3]]	Doublewide	2.928	50/49 875/864
6	<<5 1 12 -10 5 25]]	Magic	2.937	225/224 245/243
7	<<3 5 16 1 17 23]]	Porky	3.362	225/224 250/243
8	<<7 -3 8 -21 -7 27]]	Orwell	3.685	225/224 1728/1715
9	<<4 -8 14 -22 11 55]]	Shrutar	5.101	245/243 2048/2025
10	<<6 -12 10 -33 -1 57]]	Echidna	5.925	1728/1715 2048/2025
11	<<12 -2 20 -31 -2 52]]	Wizard	6.372	225/224 118098/117649
12	<<11 -11 22 -43 4 82]]	Hendecatonic	8.442	6144/6125 10976/10935
13	<<18 -14 30 -64 -3 109]]	Septisuperfourth	11.986	6144/6125 118098/117649
14	<<23 -13 42 -74 2 134]]	Fifthplus	14.679	65625/65536 420175/419904

11-limit temperaments with badness below 0.05

Listed is the wedgie and the TE complexity for 38 temperaments with badness less than 0.05.

Rank	Wedgie	Name	Complexity	Commas
1	<<6 10 10 8 2 -1 -8 -5 -16 -12]]	Hedgehog	2.439	50/49 55/54 99/98
2	<<3 5 -6 4 1 -18 -4 -28 -8 32]]	Porcupine	2.478	55/54 64/63 100/99
3	<<2 -4 -4 -12 -11 -12 -26 2 -14 -20]]	Pajara	2.543	50/49 64/63 99/98
4	<<2 -4 -4 10 -11 -12 9 2 37 42]]	Pajarous	2.718	50/49 55/54 64/63
5	<<5 1 12 14 -10 5 5 25 29 -2]]	Telepathy	2.864	55/54 99/98 176/175
6	<<1 9 -2 -6 12 -6 -13 -30 -45 -10]]	Suprapyth	3.011	55/54 64/63 99/98
7	<<3 5 16 4 1 17 -4 23 -8 -44]]	Porky	3.020	55/54 100/99 225/224
8	<<8 6 6 18 -9 -13 1 -3 21 30]]	Fleetwood	3.081	50/49 55/54 176/175
9	<<7 -3 8 2 -21 -7 -21 27 15 -22]]	Orwell	3.242	99/98 121/120 176/175
10	<<4 -8 -8 -2 -22 -24 -17 4 23 22]]	Hemipaj	3.389	50/49 64/63 121/120
11	<<8 6 6 -4 -9 -13 -34 -3 -30 -32]]	Doublewide	3.407	50/49 99/98 875/864
12	<<1 9 -2 16 12 -6 22 -30 6 52]]	Superpyth	3.410	64/63 100/99 245/243
13	<<1 -13 -2 -6 -23 -6 -13 32 31 -10]]	Quasisupra	3.490	64/63 99/98 121/120
14	<<10 2 2 6 -20 -25 -25 -1 7 10]]	Astrology	3.575	50/49 121/120 176/175
15	<<4 14 14 20 13 11 18 -7 -2 8]]		3.637	50/49 99/98 2662/2625
16	<<5 1 -10 -8 -10 -30 -30 -26 -22 12]]		3.686	64/63 100/99 605/588
17	<<5 1 12 -8 -10 5 -30 25 -22 -64]]	Magic	3.715	100/99 225/224 245/243
18	<<0 0 0 22 0 0 35 0 51 62]]		4.028	50/49 64/63 245/243
19	<<4 -8 14 -2 -22 11 -17 55 23 -54]]	Shrutar	4.530	121/120 176/175 245/243
20	<<13 7 18 10 -19 -8 -29 22 -1 -34]]		4.554	99/98 121/120 625/616
21	<<9 -7 4 -10 -32 -19 -47 29 1 -42]]		5.075	99/98 176/175 2560/2541
22	<<10 2 24 6 -20 10 -25 50 7 -66]]		5.271	121/120 225/224 245/243
23	<<2 -4 18 -12 -11 23 -26 53 -14 -96]]		5.317	100/99 385/384 1232/1215
24	<<7 -3 8 -20 -21 -7 -56 27 -36 -84]]		5.605	100/99 225/224 1728/1715
25	<<6 -12 10 -14 -33 -1 -43 57 9 -74]]	Echidna	5.898	176/175 540/539 896/891
26	<<12 -2 20 -6 -31 -2 -51 52 -7 -86]]	Wizard	6.421	225/224 385/384 4000/3993
27	<<11 -11 22 0 -43 4 -38 82 38 -76]]		7.478	121/120 176/175 10976/10935
28	<<9 -7 26 -10 -32 16 -47 80 1 -118]]		7.718	245/243 385/384 4000/3993
29	<<13 -15 18 -12 -54 -8 -64 84 24 -96]]		8.886	176/175 540/539 16384/16335
30	<<11 -11 22 -22 -43 4 -73 82 -13 -138]]		9.219	540/539 896/891 4375/4356
31	<<19 -5 28 -4 -52 -9 -72 79 8 -108]]		9.470	225/224 385/384 43923/43750
32	<<16 -10 34 -8 -53 9 -68 107 16 -140]]		10.578	385/384 3388/3375 9801/9800
33	<<18 -14 30 -20 -64 -3 -94 109 2 -160]]	Septisuperfourth	12.086	540/539 4000/3993 5632/5625
34	<<25 -17 38 -18 -85 -10 -115 136 17 -182]]		15.106	540/539 5632/5625 35937/35840
35	<<28 -12 54 -14 -84 7 -119 159 9 -226]]		16.904	385/384 9801/9800 456533/455625
36	<<30 -16 50 -26 -95 -5 -145 161 -5 -246]]		18.435	540/539 4000/3993 65625/65536
37	<<34 -24 64 -28 -117 6 -162 216 18 -300]]		22.572	5632/5625 9801/9800 41503/41472
38	<<46 -26 84 -34 -148 4 -213 268 11 -386]]		28.911	9801/9800 41503/41472 65625/65536

13-limit temperaments with badness below 0.04

Listed is the wedgie and the TE complexity for 40 temperaments with badness less than 0.04.

Rank	Wedgie	Name	Complexity	Commas
1	<<6 10 10 8 12 2 -1 -8 -3 -5 -16 -9 -12 -3 12]]	Hedgehog	2.196	50/49 55/54 65/63 99/98
2	<<2 -4 -4 10 4 -11 -12 9 -1 2 37 24 42 26 -23]]	Pajarous	2.481	50/49 55/54 64/63 65/63
3	<<3 5 -6 4 -5 1 -18 -4 -19 -28 -8 -30 32 8 -32]]	Porkpie	2.487	55/54 64/63 65/63 100/99
4	<<2 -4 -4 -12 4 -11 -12 -26 -1 2 -14 24 -20 26 58]]	Pajara	2.588	50/49 64/63 65/63 99/98
5	<<8 6 6 18 16 -9 -13 1 -4 -3 21 15 30 23 -11]]	Fleetwood	2.861	50/49 55/54 65/63 176/175
6	<<7 -3 8 2 3 -21 -7 -21 -21 27 15 18 -22 -21 3]]	Blair	2.911	65/64 78/77 91/90 99/98
7	<<5 1 12 14 -1 -10 5 5 -20 25 29 -6 -2 -47 -55]]	Telepathy	2.980	55/54 65/64 91/90 99/98
8	<<3 5 16 4 17 1 17 -4 16 23 -8 21 -44 -11 44]]		3.040	55/54 65/63 100/99 225/224
9	<<1 9 -2 -6 -9 12 -6 -13 -18 -30 -45 -54 -10 -18 -9]]		3.151	55/54 64/63 65/63 364/363
10	<<2 -4 -4 -12 -18 -11 -12 -26 -36 2 -14 -27 -20 -36 -18]]		3.161	50/49 64/63 99/98 975/968
11	<<1 -13 -2 -6 -9 -23 -6 -13 -18 32 31 27 -10 -18 -9]]		3.168	64/63 78/77 91/90 121/120
12	<<5 1 12 14 21 -10 5 5 15 25 29 45 -2 15 21]]		3.194	55/54 65/63 99/98 176/175
13	<<3 5 -6 4 17 1 -18 -4 16 -28 -8 21 32 70 44]]		3.195	55/54 64/63 91/90 100/99
14	<<1 9 -2 16 13 12 -6 22 17 -30 6 -3 52 44 -14]]		3.228	64/63 78/77 91/90 100/99
15	<<1 9 -2 -6 13 12 -6 -13 17 -30 -45 -3 -10 44 67]]		3.234	55/54 64/63 91/90 99/98
16	<<5 1 -10 -8 -1 -10 -30 -30 -20 -26 -22 -6 12 34 26]]		3.296	64/63 65/63 100/99 169/165
17	<<3 5 16 4 -5 1 17 -4 -19 23 -8 -30 -44 -73 -32]]		3.380	55/54 65/64 91/90 100/99
18	<<5 1 12 -8 -1 -10 5 -30 -20 25 -22 -6 -64 -47 26]]		3.413	65/64 78/77 91/90 100/99
19	<<0 0 0 0 22 0 0 0 35 0 0 51 0 62 76]]		3.436	50/49 55/54 64/63 99/98
20	<<4 -8 -8 -2 -14 -22 -24 -17 -37 4 23 -3 22 -10 -41]]		3.467	50/49 64/63 78/77 121/120
21	<<10 2 2 6 -2 -20 -25 -25 -40 -1 7 -12 10 -13 -29]]		3.495	50/49 65/64 78/77 121/120
22	<<8 6 6 -4 -6 -9 -13 -34 -39 -3 -30 -36 -32 -39 -6]]		3.603	50/49 78/77 99/98 875/864
23	<<6 10 10 8 -10 2 -1 -8 -38 -5 -16 -60 -12 -65 -64]]		3.844	50/49 55/54 99/98 975/968
24	<<7 -3 8 2 -19 -21 -7 -21 -56 27 15 -33 -22 -83 -73]]		4.717	99/98 121/120 176/175 275/273
25	<<4 -8 14 -2 -14 -22 11 -17 -37 55 23 -3 -54 -91 -41]]		4.806	91/90 121/120 176/175 245/243
26	<<1 -13 -2 -6 -31 -23 -6 -13 -53 32 31 -24 -10 -80 -85]]		5.065	64/63 99/98 121/120 275/273
27	<<9 -7 4 -10 -15 -32 -19 -47 -57 29 1 -9 -42 -57 -15]]		5.170	78/77 99/98 176/175 507/500
28	<<10 2 24 6 -2 -20 10 -25 -40 50 7 -12 -66 -94 -29]]		5.251	65/64 91/90 121/120 245/243
29	<<13 7 18 10 -7 -19 -8 -29 -59 22 -1 -42 -34 -86 -61]]		5.337	65/64 99/98 121/120 275/273
30	<<5 1 12 -8 -23 -10 5 -30 -55 25 -22 -57 -64 -109 -50]]		5.378	100/99 225/224 245/243 275/273
31	<<1 9 -2 16 35 12 -6 22 52 -30 6 48 52 106 62]]		5.435	64/63 100/99 245/243 275/273
32	<<6 -12 10 -14 -32 -33 -1 -43 -73 57 9 -30 -74 -127 -59]]		7.120	176/175 351/350 364/363 540/539
33	<<12 -2 20 -6 -20 -31 -2 -51 -76 52 -7 -39 -86 -130 -47]]		7.303	225/224 351/350 364/363 385/384
34	<<9 -7 26 -10 -37 -32 16 -47 -92 80 1 -60 -118 -200 -91]]		9.701	245/243 352/351 385/384 625/624
35	<<12 -2 20 -6 -42 -31 -2 -51 -111 52 -7 -90 -86 -192 -123]]		9.808	225/224 275/273 385/384 4000/3993
36	<<13 -15 18 -12 -51 -54 -8 -64 -129 84 24 -63 -96 -210 -132]]		11.639	176/175 351/350 540/539 33275/33124
37	<<19 -5 28 -4 -39 -52 -9 -72 -132 79 8 -72 -108 -213 -120]]		11.812	225/224 351/350 385/384 10648/10647
38	<<11 -11 22 -22 -55 -43 4 -73 -128 82 -13 -87 -138 -236 -109]]		12.215	352/351 364/363 540/539 625/624
39	<<16 -10 34 -8 -56 -53 9 -68 -148 107 16 -93 -140 -283 -164]]		14.161	352/351 385/384 625/624 4459/4455
40	<<18 -14 30 -20 -52 -64 -3 -94 -149 109 2 -69 -160 -257 -106]]		14.257	351/350 364/363 540/539 4096/4095